Stable Degenerations of Surfaces Isogenous to a Product II

TL;DR

This paper investigates the singularities of stable surfaces on the boundary of the moduli space of surfaces isogenous to a product and uses deformation theory to identify connected components of this space.

Contribution

It characterizes possible singularities and applies $ ext{Q}$-Gorenstein deformation theory to find new connected components of the moduli space.

Findings

Classification of singularities on boundary stable surfaces

Identification of connected components in the moduli space

Application of $ ext{Q}$-Gorenstein deformation theory

Abstract

In this note, we describe the possible singularities on a stable surface which is in the boundary of the moduli space of surfaces isogenous to a product. Then we use the $\mathbb Q$-Gorenstein deformation theory to get some connected components of the moduli space of stable surfaces.